Question

If $\angle$A = 30$°$ then show that sinA = $\sqrt{\frac{1-\cos 2A}{2}}$

Answer 1

$$\begin{gathered} \mathrm{Given}:\angle \mathrm{A}=30° \\ \mathrm{To}\mathrm{show}:\sin \mathrm{A}=\sqrt{\frac{1-\cos 2\mathrm{A}}{2}} \\ \mathrm{LHS}:\sin \mathrm{A}=\sin 30°=\frac{1}{2} \\ \mathrm{RHS}:\hspace{0.17em}\sqrt{\frac{1-\cos 2\mathrm{A}}{2}} \\ =\sqrt{\frac{1-\cos \left(2\times 30\right)°}{2}} \\ =\sqrt{\frac{1-\cos 60°}{2}} \\ =\sqrt{\frac{1-{\displaystyle \frac{1}{2}}}{2}} \\ =\sqrt{\frac{1}{4}}=\frac{1}{2} \\ \mathrm{Thus},\mathrm{LHS}=\mathrm{RHS} \\ \mathrm{Hence}\mathrm{proved}. \end{gathered}$$